The single unifying factor for all stories involving a post-apocalyptic world is the sudden rapid destruction of a majority of the population, resulting in the remains of humanity existing in isolated pockets. Everything else is flavor.

Perhaps the most famous vision is to be found in movies such as Mad Max and Green Legend Ran, and roleplaying games such as Fallout, Wasteland, and Dark Sun. It usually occurs after a nuclear holocaust, with the world stripped bare, converted to a massive nuclear desert. This world can also be a result of a more mundane depletion of the Earth's resources. In any case, the world is bleak, and often violent. Survival goes to the fittest.

In films such as The Stand and Akira, and stories such as those found on www.theblink.com, the eradication of humanity has no effect on the technology we have produced, other than most of it will no longer be maintained. This type of future can have biological or ecological foundations, or it may be fallout from some major war that claimed most human life. Sometimes the aftermath of a religious judgement day is portrayed like this, as well, although most versions add demonic hordes.

Are post-apocalyptic stories pessimistic? I'd argue that they are more optimistic than they might first appear. Post-apocalyptic stories all have as a basic assumption that humanity manages to survive huge catastrophes. Not only does humanity survive, but it then procedes to surmount the odds and pull itself back together, albeit with no small amount of violence. Usually the dénoument of a post-apocalyptic story involves the return of something resembling "culture" to humanity, and the heroic characters are usually marked by a humanistic streak that puts them rather out of place in their world, but more in place in ours.